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Physics - Topic 5 - Forces (Resultant Forces (Scale Drawings (1) Draw all…
Physics - Topic 5 - Forces
Contact and Non-Contact Forces
Vectors
Force is a vector quantity.
Vector quantities have a
magnitude
and a
direction
.
Physical quantities
, some are vector, some are scalar (have
magnitude
and
no direction.
Physical (Vector)
Force
Velocity
Displacement
Acceleration
Momentum
Physical (Scalar)
Speed
Distance
Mass
Temperature
Time
Usually
represented by an arrow
-
length = magnitude,
arrow direction = direction of the quantity.
Forces (can be contact or non-contact)
A force is a push or pull on an object that is caused by it interacting with something.
When two objects
have to be touching
for a force to act, the force is called a
contact
force.
E.g. friction, air resistance, tension in ropes etc.
If the objects
do not need to be touching
for the force to act, the force is a
non-contact
force.
E.g. magnetic force, gravitational force, electrostatic force etc.
A force is produced on
both objects
when two objects interact.
An
interaction pair
is a pair of forces that are
equal
and
opposite
and act on two interacting objects - this is basically
Newton's Third Law
Weight, Mass and Gravity
Gravitational Force
You
only notice gravity
when one of the
masses
it attracts is
really big
, such as a
planet
.
Anything near
a
planet
or
star
is attracted to gravity
very strongly.
This has
two important effects:
On the
surface of a planet
, it makes all things
fall towards the ground.
It
gives everything a weight.
Weight and Mass
Mass is the amount of 'stuff' in an objec
t whereas
weight is the force acting on an object due to gravity.
Close to Earth, this force is caused by the gravitational field around the Earth.
Gravitational field strength (GFS)
varies with location; it's
stronger the closer you are to the mass
causing the field, and stronger for larger masses.
The
weight
of an object
depends on the strength of the gravitational field
at the
location
of the object. This means that the
weight of an object changes with its location.
Weight is a force
measured in newtons. The
centre of mass
is a point at which you can assume the
whole mass in concentrated.
For a uniform object, this will be the at the centre of the object
The
weight of an object and the mass of an object are directly proportional.
This can be written as W (proportional symbol) m
Weight is measured using a
calibrated spring-balance, also known as a
newtonmeter
.
Resultant Forces
A
number of forces acting on an object
may be
replaced by a single force
that has the
same effect
as all the original forces acting together.
This single force is called the resultant force.
Free Body diagrams
show
all the forces
acting on an object.
When a force moves an object through a distance, ENERGY IS TRANSFERRED and WORK IS DONE on the object.
A
single force can be resolved
into
two components
acting at
right angles
to each other. The two component forces together have the
same effect as the single force.
Scale Drawings
1) Draw all the forces acting on an object, to scale.
2) Then draw a straight line from the start of the first force to the end of the last force - this is the resultant force.
3) Measure the length of the resultant force on the diagram to find the magnitude and the angle to find the direction of the force.
If all of the forces acting on an object combine to give a resultant force of zero, the object is in equilibrium.
Distance, Displacement, Speed and Velocity
Speed and Velocity are Both How Fast You’re Going
This means you can have objects travelling at a constant speed with a changing velocity.
s = vt /// distance travelled (m) = speed (m/s) × time (s)
Objects rarely travel at a constant speed.
Speed and velocity both measure how fast you’re going, but speed is a scalar and velocity is a vector.
Distance is Scalar, Displacement is a Vector
Displacement is a vector quantity. It measures the distance and direction in a straight line from an object’s starting point to its finishing point.
If you walk 5 m north, then 5 m south, your displacement is 0 m but the distance travelled is 10 m.
Distance is just how far an object has moved.
Fluid Pressure
Pressure is the Force per Unit Area
Pressure is force per unit area, so this means the particles exert a pressure.
The pressure of a fluid means a force is exerted normal
(at right angles) to any surface in contact with the fluid.
They collide with surfaces and other particles.
p = f/a /// pressure in pascals =Force normal to
a surface/ Area of that surface
Fluids are particles are able to move around.
Pressure in a Liquid Depends on Depth and Density
The more dense, the more particles it has in a space, making pressure higher.
As the depth increases, the number of particles above that point increases. Weight add pressure.
Density is a measure of the how close together the particles
in a substance are.
p = hpg
Pressure (Pa) = Height of the column x Gravitational field strength x Density of the liquid
Distance-Time and Velocity-Time Graphs
You Can Show Journeys on Distance-Time Graphs
If the object is changing speed you can find its speed at a point by finding the gradient of the tangent to the curve at that point.
Gradient = speed
Flat sections are where it’s stationary — it’s stopped.
Straight uphill sections mean it is travelling at a steady speed.
Curves represent acceleration or deceleration
A steepening curve means it’s speeding up (increasing gradient).
A levelling off curve means it’s slowing down.
You Can Also Show them on a Velocity-Time Graph
Gradient = acceleration, since acceleration is change in velocity ÷ time.
Flat sections represent travelling at a steady speed.
The steeper the graph, the greater the acceleration or deceleration.
Uphill sections (/) are acceleration.
Downhill sections () are deceleration.
A curve means changing acceleration.If the graph is curved, you can use a tangent to the curve at a point to fnd the acceleration at that point.
The area under any section of the graph (or all of it) is equal to the distance travelled in that time interval
If the section under the graph is irregular, it’s easier to find the area by counting the squares under the line and multiplying the number by the value of one square.
Acceleration
Acceleration is How Quickly You’re Speeding Up
Acceleration is the change in velocity in a certain amount of time
a = v/t ///// Acceleration = Change in velocity / time
Acceleration is definitely not the same as velocity or speed.
Deceleration is just negative acceleration (velocity is negative)
Uniform Acceleration Means a Constant Acceleration
Acceleration due to gravity (roughly equal to 9.8 m/s2)
v2 – u2 = 2as /// Final velocity^2 - Initial velocity^2 = 2x Acceleration x distance
Constant acceleration is sometimes called uniform acceleration.
You Need to be Able to Estimate Accelerations
You might have to estimate the acceleration (or deceleration) of an object.
Upthrust and Atmospheric Pressure
An Object Floats if its Weight = Upthrust
if it floats depends on its density.
If an object’s weight is more than the upthrust, the object sinks.
The object’s weight is equal to the upthrust, so the object floats.
If the upthrust on an object is equal to the object’s weight, then the forces balance and the object floats.
A denser object cant displace enough fluid to its weight so it sinks.
A less dense object placed in fluid weighs less.
Atmospheric Pressure Decreases with Height
As the altitude increases, atmospheric pressure decreases.
As the altitude increases, the atmosphere gets less dense, so fewer air molecules.
Atmospheric pressure is created on a surface
by air molecules colliding with the surface.
There are also fewer air molecules above a surface as the height increases.
The atmosphere is a layer of air that surrounds Earth.
Objects in Fluids Experience Upthrust
Pressure increases with depth so pressure on the bottom is greater than the top.
This causes a resultant force upwards, known as upthrust.
When an object is submerged in a fluid there is pressure in every direction.
The upthrust is equal to the weight of fluid that has been displaced by the object.
Investigating Motion
Practial
Newton’s First and Second Laws
If the resultant force on a stationary object is zero, the object will remain stationary. If the resultant force on a moving object is zero, it’ll just carry on moving at the same velocity (same speed and direction).
This “acceleration” can take five different forms: starting,
stopping, speeding up, slowing down and changing direction.
On a free body diagram, the arrows will be unequal.
A non-zero resultant force will always produce acceleration (or deceleration) in the direction of the force.
Acceleration is Proportional to the Resultant Force
Acceleration is also inversely proportional to the mass of the object so an object with a larger mass will accelerate less than one with a smaller mass.
F = ma /// resultant force = acceleration x mass
The larger the resultant force acting on an object, the more the object accelerates the force and the acceleration are directly proportional.
Terminal Velocity
Drag Increases as Speed Increases
Important factor by far in reducing drag is keeping the shape of the object streamlined. Parachutes work in the opposite way.
Frictional forces from fluids always increase with speed.
Drag is the resistance you get in a fluid. Air resistance is a type of drag
Objects Falling Through Fluids Reach a Terminal Velocity
As the speed increases the friction builds up reducing the acceleration until the friction force is equal.
It will have reached its maximum speed or terminal velocity and will fall at a steady speed
When a object falls, the force of gravity is much more than the frictional force slowing it down.
Friction is Always There to Slow Things Down
Friction always acts in the opposite direction to movement.
To travel at a steady speed, the driving force needs to balance the frictional forces.
If an object has no force propelling it along it will always slow down and stop because of friction.
You get friction between two surfaces in contact, or when an object passes through a fluid.
Terminal Velocity Depends on Shape and Area
Everything doesn't fall at the same rate due to air resistance.
The terminal velocity of any object is determined by its drag in comparison to its weight.
The accelerating force acting on all falling objects is gravity.
The frictional force depends on its shape and area.
Inertia and Newton’s Third Law
Inertia is the Tendency for Motion to Remain Unchanged
An object’s inertial mass measures how difficult it is to change the velocity of an object.
Inertial mass can be found using Newton’s Second Law of F = ma
Upon by a resultant force, objects at rest stay at rest and objects moving at a steady speed will stay moving at that speed continue in the same state of motion is called inertia.
Newton’s Third Law: Equal and Opposite Forces Act on Interacting Objects
When two objects interact, the forces they
exert on each other are equal and opposite.
As soon as you stop pushing so does the item.
The important thing to remember is that the two forces are acting on different objects.
If you push something, it will push back against you, just as hard.
Reaction Times
Reaction Times Vary From Person to Person
This can be affected by tiredness, drugs or alcohol. Distractions can also affect your ability to react.
For the ruler drop test you have to do many repeats in the exact same conditions to make it a fair test, also doing it under different conditions to see how it effects it.
Momentum
Momentum = Mass × Velocity
Momentum is a vector quantity — it has size and direction.
p = mv momentum (kg m/s) = mass (kg) × velocity (m/s)
The greater the mass of an object, or the greater its velocity, the more momentum the object has.
Momentum Before = Momentum After
In a closed system, the total momentum before an event (e.g. a collision) is the same as after the event. This is called conservation of momentum.
A closed system is just a fancy way of saying that no external forces act. If the momentum before an event is zero, then the momentum after will also be zero.
e.g in an explosion, the momentum before is zero. After the explosion, the pieces fly off in different directions, so that the total momentum cancels out to zero.
Stopping Distances
Many Factors Affect Your Total Stopping Distance
Stopping Distance = Thinking Distance + Braking Distance::::: Thinking distance is affected by your speed and reaction time. Your Braking distance is affected by your speed, weather, tyres, brakes.
You need to be able to describe the factors affecting stopping distance and how this affects safety — especially in an emergency.
The longer it takes to perform an emergency stop, the higher the risk of crashing into whatever’s in front.
Speed limits are really important because speed affects the stopping distance so much.
Braking Relies on Friction Between the Brakes and Wheels
The faster a vehicle is going the more kinetic energy it has, so the more work is needed for it to be stopped.
A larger braking force means a larger deceleration. Very large decelerations may cause brakes to overheat and skid.
When the brake pedal is pushed, this causes brake pads to be pressed onto the wheels This contact causes friction, which causes work to be done. The brakes increase in temp.
More on Stopping Distances
Speed Affects Braking Distance More Than Thinking Distance
The work done to stop the car is equal
to the energy in the car’s kinetic energy store So as speed doubles, the kinetic energy increases
x4, and so the work done to stop the car is x4, so the braking distance x4.
Stopping distance is a combination of these two distances so the graph of speed against stopping distance for a car looks like this:
This is because the thinking time stays pretty
constant.
You need to be able to interpret graphs like this for a range of vehicles — they’re all a similar shape.
As a car speeds up, the thinking distance increases at the
same rate as speed. The graph is linear
Investigating Springs
Practical page 56
Work Out Energy Stored for Linear Relationships
If the spring is not stretched past its limit of proportionality, the work done can be done by using
E = 1/2ke^2/// elastic potential energy = 1/2x spring constant x extension^2
Calculating Forces
An Object is in Equilibrium if the Forces on it are Balanced
On a scale diagram, this means that the tip of the last force you
draw should end where the tail of the first force you drew begins.
If the forces combine to make 0 the object is in equilibrium.
You Can Split a Force into Components
Split them into two components at right angles to each other.
Acting together, these components have the same effect as the single force.
Some forces act at angles.
Draw the force to scale, and then add the horizontal and vertical
components along the grid lines. Then you can just measure them. To resolve a force.
Use Scale Drawings to Find Resultant Forces
2) Draw a straight line from the start of the first force to the
end of the last force — this is the resultant force
3) Measure the length of the resultant force on the diagram to find
the magnitude and the angle to find the direction of the force
1) Draw all the forces acting on an object, to scale, tip-to-tail.
Moments
Levers Make it Easier for us to Do Work
Levers increase the distance from the pivot at which
the force is applied.
M = Fd this means less force is needed to get the same moment.
Gears Transmit Rotational Effects
They are used to transmit the rotational effect of a force from one place to another.
Bigger gear cause a bigger moment of force as the distance to the pivot is greater.
Their teeth interlock so that turning one causes another to turn, in the opposite direction.
The larger gear will turn slower than the smaller gear.
A Moment is the Turning Effect of a Force
If the total anticlockwise moment equals the total clockwise moment about a pivot, the object is balanced and won’t turn.
You can use the equation above to find a missing force or distance in these situations.
M = Fd /// moments of a force = force x distance
Forces and Elasticity
Extension is Directly Proportional to Force
F=k x e/////force = spring constant x extension
The spring constant depends on the material that you are
stretching.
The extension of a stretched spring is
directly proportional to the load or force applied — so F e
The equation also works for compression
but this Stops Working when the Force is Great Enough
There is a maximum point for force against extension, where the graph would curve and is know as limit of proportionality.
Stretching, Compressing or Bending Transfers Energy
An elastically deformed object if it can go back to its
original shape and length after the force has been removed.
Objects that can be elastically deformed are called elastic objects
You need more than one force acting
on the object so it doesn't just move.
If a object has been inelastically deformed if it doesn’t return to its
original shape even if force if removed.
When you apply a force it can stretch, compress or bend.
If it is elastically deformed, ALL this energy is transferred
to the object’s elastic potential energy store.
Changes in Momentum
You Can Use Conservation of Momentum to Calculate Velocities or Masses
You’ve already seen that momentum is conserved in a closed system. You can use this to help you calculate things like the velocity or mass of objects in an event.
Forces Cause a Change in Momentum
The force causing the change is equal to the rate of change of momentum.
A larger force means a faster change of momentum.
Force = Change in momentum / Change in
time
if someone’s momentum changes very quickly (like in a car crash), the forces on the body will be very large, and more likely to cause injury.
You also know that F = ma and that a = change in velocity ÷ change in time.
This is why cars are designed to slow people down over a longer time when they have a crash by using seat belts and air bags.
You know that when a non-zero resultant force acts on a moving object it causes its velocity to change.This means that there is a change in momentum.
REMEMBER THIS EQUATION
Weight = Mass x Gravitational Field Strength
OR
W = m g
weight, W, in newtons, N
mass, m, in kilograms, kg
Gravitational Field Strength, g, in newtons per kilogram, N/kg (you will be given the value of this)
REMEMBER THIS EQUATION
Work Done = Force x Distance
OR
W = Fs
work done, W, in joules, J
force, F, in newtons, N
distance, s, in metres, m
